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Let <math>G(V,E)</math> be a [[graph (mathematics)|graph]] and <math>M</math> a [[Matching (graph theory)|matching]] in <math>G</math>. A vertex <math>v\in V(G)</math> is said to be '''saturated''' by <math>M</math> if there is an edge in <math>M</math> incident to <math>v</math>. A vertex <math>v\in V(G)</math> with no such edge is said to be '''unsaturated''' by <math>M</math>. We also say that <math>M</math> '''saturates''' <math>v</math>.<ref>[http://planetmath.org/?op=getobj&from=objects&id=4735 Saturate]. [[PlanetMath]].</ref> | |||
==See also== | |||
* [[Hall's marriage theorem]] | |||
* [[Bipartite matching]] | |||
==References== | |||
{{reflist}} | |||
[[Category:Matching]] | |||
Revision as of 10:10, 24 September 2013
Let be a graph and a matching in . A vertex is said to be saturated by if there is an edge in incident to . A vertex with no such edge is said to be unsaturated by . We also say that saturates .[1]
See also
References
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